Lots of good suggestions already. If you go to Rutland Water (near Oakham) you can visit Barnsdale Gardens, of Geof Hamilton fame, now run by son and dil. There is a coffee/lunch place there, but Bansdale Lodge just 1 mile away is much better.
Stamford is fabulous, as is Burleigh House, the grand place of William Cecil, Queen Elisabeth's adviser- there is a tea/lunch place inside- but the very old and grand George Hotel on the same side of town- is a magnificent experience.
And of course, the easiest would be a day in Cambridge, if you have not yet visited- wonderful. You can park and ride, much easier than parking in town.
If you do go there, find your way to the round Church, and ask them to put on the video on the history of Cambridge- then go and visit Kings College Chapel. If you can, wait till 5pm and go to Evensong there- free of charge, candle lit and with (pared during week days) Kings college choir singing. It only last 30 mins- then you still have plenty of time to get to Stansted and dinner at 8ish.